Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 24 Jan 2010 07:22:10 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/24/t1264343040sd44hnhdv00vx5g.htm/, Retrieved Thu, 02 May 2024 23:26:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72409, Retrieved Thu, 02 May 2024 23:26:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact196
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [aantal bezoekers ...] [2010-01-24 14:22:10] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
6715
7703
9856
8326
9269
7035
10342
11682
10304
11385
9777
8882
7897
6930
9545
9110
7459
7320
10017
12307
11072
10749
9589
9080
7384
8062
8511
8684
8306
7643
10577
13747
11783
11611
9946
8693
7303
7609
9423
8584
7586
6843
11811
13414
12103
11501
8213
7982
7687
7180
7862
8043
8340
6692
10065
12684
11587
9843
8110
7940
6475
6121
9669
7778
7826
7403
10741
14023
11519
10236
8075
8157




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72409&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72409&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72409&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.105565855420786
beta0
gamma0.649886178771197

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.105565855420786 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.649886178771197 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72409&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.105565855420786[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.649886178771197[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72409&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72409&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.105565855420786
beta0
gamma0.649886178771197







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1378978049.3170405983-152.317040598293
1469307046.48421109652-116.48421109652
1595459583.89243822658-38.8924382265832
1691109132.03337389994-22.0333738999434
1774597505.78738445388-46.7873844538753
1873207354.17821670858-34.1782167085821
191001710291.0668132091-274.066813209136
201230711577.8396981477729.160301852255
211107210314.7274450025757.272554997526
221074911448.7078859083-699.70788590829
2395899802.33927357186-213.339273571859
2490808941.10624651321138.893753486787
2573847876.64309174713-492.643091747132
2680626858.712372583511203.28762741649
2785119580.54601867563-1069.54601867563
2886849029.68497094595-345.684970945955
2983067354.8834029306951.116597069407
3076437315.94828454679327.051715453214
311057710151.5278912971425.472108702919
321374712095.30444800681651.69555199322
331178310945.9215191251837.078480874921
341161111241.4125843075369.587415692478
3599469990.64158105826-44.6415810582585
3686939351.96342098732-658.963420987318
3773037836.17380841848-533.173808418475
3876097799.77569658483-190.775696584833
3994239053.29023083748369.709769162524
4085849075.13168247993-491.131682479934
4175868138.78122705509-552.78122705509
4268437578.32917164003-735.329171640026
431181110358.96747567461452.03252432537
441341413123.8934001608290.106599839155
451210311357.2522413304745.747758669617
461150111371.3585127622129.641487237841
4782139854.47422021005-1641.47422021005
4879828690.13181891705-708.131818917054
4976877242.27073720966444.729262790337
5071807508.13510703508-328.135107035082
5178629072.94838683614-1210.94838683614
5280438427.53605476578-384.536054765782
5383407466.60278675041873.397213249588
5466926950.59493824193-258.594938241931
551006511053.0305555986-988.030555598592
561268412884.9643811143-200.964381114252
571158711331.3381638754255.6618361246
58984310935.5776029209-1092.57760292092
5981108260.15388030792-150.153880307920
6079407795.77761992109144.222380078911
6164757108.0315756788-633.031575678803
6261216810.87029959265-689.870299592649
6396697824.334648203071844.66535179693
6477787981.86807563744-203.868075637438
6578267771.2191159778554.7808840221469
6674036510.78849694748892.211503052522
671074110310.7033617456430.296638254384
681402312749.87024233441273.12975766564
691151911617.2858987291-98.285898729071
701023610400.4553976088-164.455397608761
7180758370.82211703647-295.822117036469
7281578062.1834116001694.8165883998354

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7897 & 8049.3170405983 & -152.317040598293 \tabularnewline
14 & 6930 & 7046.48421109652 & -116.48421109652 \tabularnewline
15 & 9545 & 9583.89243822658 & -38.8924382265832 \tabularnewline
16 & 9110 & 9132.03337389994 & -22.0333738999434 \tabularnewline
17 & 7459 & 7505.78738445388 & -46.7873844538753 \tabularnewline
18 & 7320 & 7354.17821670858 & -34.1782167085821 \tabularnewline
19 & 10017 & 10291.0668132091 & -274.066813209136 \tabularnewline
20 & 12307 & 11577.8396981477 & 729.160301852255 \tabularnewline
21 & 11072 & 10314.7274450025 & 757.272554997526 \tabularnewline
22 & 10749 & 11448.7078859083 & -699.70788590829 \tabularnewline
23 & 9589 & 9802.33927357186 & -213.339273571859 \tabularnewline
24 & 9080 & 8941.10624651321 & 138.893753486787 \tabularnewline
25 & 7384 & 7876.64309174713 & -492.643091747132 \tabularnewline
26 & 8062 & 6858.71237258351 & 1203.28762741649 \tabularnewline
27 & 8511 & 9580.54601867563 & -1069.54601867563 \tabularnewline
28 & 8684 & 9029.68497094595 & -345.684970945955 \tabularnewline
29 & 8306 & 7354.8834029306 & 951.116597069407 \tabularnewline
30 & 7643 & 7315.94828454679 & 327.051715453214 \tabularnewline
31 & 10577 & 10151.5278912971 & 425.472108702919 \tabularnewline
32 & 13747 & 12095.3044480068 & 1651.69555199322 \tabularnewline
33 & 11783 & 10945.9215191251 & 837.078480874921 \tabularnewline
34 & 11611 & 11241.4125843075 & 369.587415692478 \tabularnewline
35 & 9946 & 9990.64158105826 & -44.6415810582585 \tabularnewline
36 & 8693 & 9351.96342098732 & -658.963420987318 \tabularnewline
37 & 7303 & 7836.17380841848 & -533.173808418475 \tabularnewline
38 & 7609 & 7799.77569658483 & -190.775696584833 \tabularnewline
39 & 9423 & 9053.29023083748 & 369.709769162524 \tabularnewline
40 & 8584 & 9075.13168247993 & -491.131682479934 \tabularnewline
41 & 7586 & 8138.78122705509 & -552.78122705509 \tabularnewline
42 & 6843 & 7578.32917164003 & -735.329171640026 \tabularnewline
43 & 11811 & 10358.9674756746 & 1452.03252432537 \tabularnewline
44 & 13414 & 13123.8934001608 & 290.106599839155 \tabularnewline
45 & 12103 & 11357.2522413304 & 745.747758669617 \tabularnewline
46 & 11501 & 11371.3585127622 & 129.641487237841 \tabularnewline
47 & 8213 & 9854.47422021005 & -1641.47422021005 \tabularnewline
48 & 7982 & 8690.13181891705 & -708.131818917054 \tabularnewline
49 & 7687 & 7242.27073720966 & 444.729262790337 \tabularnewline
50 & 7180 & 7508.13510703508 & -328.135107035082 \tabularnewline
51 & 7862 & 9072.94838683614 & -1210.94838683614 \tabularnewline
52 & 8043 & 8427.53605476578 & -384.536054765782 \tabularnewline
53 & 8340 & 7466.60278675041 & 873.397213249588 \tabularnewline
54 & 6692 & 6950.59493824193 & -258.594938241931 \tabularnewline
55 & 10065 & 11053.0305555986 & -988.030555598592 \tabularnewline
56 & 12684 & 12884.9643811143 & -200.964381114252 \tabularnewline
57 & 11587 & 11331.3381638754 & 255.6618361246 \tabularnewline
58 & 9843 & 10935.5776029209 & -1092.57760292092 \tabularnewline
59 & 8110 & 8260.15388030792 & -150.153880307920 \tabularnewline
60 & 7940 & 7795.77761992109 & 144.222380078911 \tabularnewline
61 & 6475 & 7108.0315756788 & -633.031575678803 \tabularnewline
62 & 6121 & 6810.87029959265 & -689.870299592649 \tabularnewline
63 & 9669 & 7824.33464820307 & 1844.66535179693 \tabularnewline
64 & 7778 & 7981.86807563744 & -203.868075637438 \tabularnewline
65 & 7826 & 7771.21911597785 & 54.7808840221469 \tabularnewline
66 & 7403 & 6510.78849694748 & 892.211503052522 \tabularnewline
67 & 10741 & 10310.7033617456 & 430.296638254384 \tabularnewline
68 & 14023 & 12749.8702423344 & 1273.12975766564 \tabularnewline
69 & 11519 & 11617.2858987291 & -98.285898729071 \tabularnewline
70 & 10236 & 10400.4553976088 & -164.455397608761 \tabularnewline
71 & 8075 & 8370.82211703647 & -295.822117036469 \tabularnewline
72 & 8157 & 8062.18341160016 & 94.8165883998354 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72409&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]7897[/C][C]8049.3170405983[/C][C]-152.317040598293[/C][/ROW]
[ROW][C]14[/C][C]6930[/C][C]7046.48421109652[/C][C]-116.48421109652[/C][/ROW]
[ROW][C]15[/C][C]9545[/C][C]9583.89243822658[/C][C]-38.8924382265832[/C][/ROW]
[ROW][C]16[/C][C]9110[/C][C]9132.03337389994[/C][C]-22.0333738999434[/C][/ROW]
[ROW][C]17[/C][C]7459[/C][C]7505.78738445388[/C][C]-46.7873844538753[/C][/ROW]
[ROW][C]18[/C][C]7320[/C][C]7354.17821670858[/C][C]-34.1782167085821[/C][/ROW]
[ROW][C]19[/C][C]10017[/C][C]10291.0668132091[/C][C]-274.066813209136[/C][/ROW]
[ROW][C]20[/C][C]12307[/C][C]11577.8396981477[/C][C]729.160301852255[/C][/ROW]
[ROW][C]21[/C][C]11072[/C][C]10314.7274450025[/C][C]757.272554997526[/C][/ROW]
[ROW][C]22[/C][C]10749[/C][C]11448.7078859083[/C][C]-699.70788590829[/C][/ROW]
[ROW][C]23[/C][C]9589[/C][C]9802.33927357186[/C][C]-213.339273571859[/C][/ROW]
[ROW][C]24[/C][C]9080[/C][C]8941.10624651321[/C][C]138.893753486787[/C][/ROW]
[ROW][C]25[/C][C]7384[/C][C]7876.64309174713[/C][C]-492.643091747132[/C][/ROW]
[ROW][C]26[/C][C]8062[/C][C]6858.71237258351[/C][C]1203.28762741649[/C][/ROW]
[ROW][C]27[/C][C]8511[/C][C]9580.54601867563[/C][C]-1069.54601867563[/C][/ROW]
[ROW][C]28[/C][C]8684[/C][C]9029.68497094595[/C][C]-345.684970945955[/C][/ROW]
[ROW][C]29[/C][C]8306[/C][C]7354.8834029306[/C][C]951.116597069407[/C][/ROW]
[ROW][C]30[/C][C]7643[/C][C]7315.94828454679[/C][C]327.051715453214[/C][/ROW]
[ROW][C]31[/C][C]10577[/C][C]10151.5278912971[/C][C]425.472108702919[/C][/ROW]
[ROW][C]32[/C][C]13747[/C][C]12095.3044480068[/C][C]1651.69555199322[/C][/ROW]
[ROW][C]33[/C][C]11783[/C][C]10945.9215191251[/C][C]837.078480874921[/C][/ROW]
[ROW][C]34[/C][C]11611[/C][C]11241.4125843075[/C][C]369.587415692478[/C][/ROW]
[ROW][C]35[/C][C]9946[/C][C]9990.64158105826[/C][C]-44.6415810582585[/C][/ROW]
[ROW][C]36[/C][C]8693[/C][C]9351.96342098732[/C][C]-658.963420987318[/C][/ROW]
[ROW][C]37[/C][C]7303[/C][C]7836.17380841848[/C][C]-533.173808418475[/C][/ROW]
[ROW][C]38[/C][C]7609[/C][C]7799.77569658483[/C][C]-190.775696584833[/C][/ROW]
[ROW][C]39[/C][C]9423[/C][C]9053.29023083748[/C][C]369.709769162524[/C][/ROW]
[ROW][C]40[/C][C]8584[/C][C]9075.13168247993[/C][C]-491.131682479934[/C][/ROW]
[ROW][C]41[/C][C]7586[/C][C]8138.78122705509[/C][C]-552.78122705509[/C][/ROW]
[ROW][C]42[/C][C]6843[/C][C]7578.32917164003[/C][C]-735.329171640026[/C][/ROW]
[ROW][C]43[/C][C]11811[/C][C]10358.9674756746[/C][C]1452.03252432537[/C][/ROW]
[ROW][C]44[/C][C]13414[/C][C]13123.8934001608[/C][C]290.106599839155[/C][/ROW]
[ROW][C]45[/C][C]12103[/C][C]11357.2522413304[/C][C]745.747758669617[/C][/ROW]
[ROW][C]46[/C][C]11501[/C][C]11371.3585127622[/C][C]129.641487237841[/C][/ROW]
[ROW][C]47[/C][C]8213[/C][C]9854.47422021005[/C][C]-1641.47422021005[/C][/ROW]
[ROW][C]48[/C][C]7982[/C][C]8690.13181891705[/C][C]-708.131818917054[/C][/ROW]
[ROW][C]49[/C][C]7687[/C][C]7242.27073720966[/C][C]444.729262790337[/C][/ROW]
[ROW][C]50[/C][C]7180[/C][C]7508.13510703508[/C][C]-328.135107035082[/C][/ROW]
[ROW][C]51[/C][C]7862[/C][C]9072.94838683614[/C][C]-1210.94838683614[/C][/ROW]
[ROW][C]52[/C][C]8043[/C][C]8427.53605476578[/C][C]-384.536054765782[/C][/ROW]
[ROW][C]53[/C][C]8340[/C][C]7466.60278675041[/C][C]873.397213249588[/C][/ROW]
[ROW][C]54[/C][C]6692[/C][C]6950.59493824193[/C][C]-258.594938241931[/C][/ROW]
[ROW][C]55[/C][C]10065[/C][C]11053.0305555986[/C][C]-988.030555598592[/C][/ROW]
[ROW][C]56[/C][C]12684[/C][C]12884.9643811143[/C][C]-200.964381114252[/C][/ROW]
[ROW][C]57[/C][C]11587[/C][C]11331.3381638754[/C][C]255.6618361246[/C][/ROW]
[ROW][C]58[/C][C]9843[/C][C]10935.5776029209[/C][C]-1092.57760292092[/C][/ROW]
[ROW][C]59[/C][C]8110[/C][C]8260.15388030792[/C][C]-150.153880307920[/C][/ROW]
[ROW][C]60[/C][C]7940[/C][C]7795.77761992109[/C][C]144.222380078911[/C][/ROW]
[ROW][C]61[/C][C]6475[/C][C]7108.0315756788[/C][C]-633.031575678803[/C][/ROW]
[ROW][C]62[/C][C]6121[/C][C]6810.87029959265[/C][C]-689.870299592649[/C][/ROW]
[ROW][C]63[/C][C]9669[/C][C]7824.33464820307[/C][C]1844.66535179693[/C][/ROW]
[ROW][C]64[/C][C]7778[/C][C]7981.86807563744[/C][C]-203.868075637438[/C][/ROW]
[ROW][C]65[/C][C]7826[/C][C]7771.21911597785[/C][C]54.7808840221469[/C][/ROW]
[ROW][C]66[/C][C]7403[/C][C]6510.78849694748[/C][C]892.211503052522[/C][/ROW]
[ROW][C]67[/C][C]10741[/C][C]10310.7033617456[/C][C]430.296638254384[/C][/ROW]
[ROW][C]68[/C][C]14023[/C][C]12749.8702423344[/C][C]1273.12975766564[/C][/ROW]
[ROW][C]69[/C][C]11519[/C][C]11617.2858987291[/C][C]-98.285898729071[/C][/ROW]
[ROW][C]70[/C][C]10236[/C][C]10400.4553976088[/C][C]-164.455397608761[/C][/ROW]
[ROW][C]71[/C][C]8075[/C][C]8370.82211703647[/C][C]-295.822117036469[/C][/ROW]
[ROW][C]72[/C][C]8157[/C][C]8062.18341160016[/C][C]94.8165883998354[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72409&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72409&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1378978049.3170405983-152.317040598293
1469307046.48421109652-116.48421109652
1595459583.89243822658-38.8924382265832
1691109132.03337389994-22.0333738999434
1774597505.78738445388-46.7873844538753
1873207354.17821670858-34.1782167085821
191001710291.0668132091-274.066813209136
201230711577.8396981477729.160301852255
211107210314.7274450025757.272554997526
221074911448.7078859083-699.70788590829
2395899802.33927357186-213.339273571859
2490808941.10624651321138.893753486787
2573847876.64309174713-492.643091747132
2680626858.712372583511203.28762741649
2785119580.54601867563-1069.54601867563
2886849029.68497094595-345.684970945955
2983067354.8834029306951.116597069407
3076437315.94828454679327.051715453214
311057710151.5278912971425.472108702919
321374712095.30444800681651.69555199322
331178310945.9215191251837.078480874921
341161111241.4125843075369.587415692478
3599469990.64158105826-44.6415810582585
3686939351.96342098732-658.963420987318
3773037836.17380841848-533.173808418475
3876097799.77569658483-190.775696584833
3994239053.29023083748369.709769162524
4085849075.13168247993-491.131682479934
4175868138.78122705509-552.78122705509
4268437578.32917164003-735.329171640026
431181110358.96747567461452.03252432537
441341413123.8934001608290.106599839155
451210311357.2522413304745.747758669617
461150111371.3585127622129.641487237841
4782139854.47422021005-1641.47422021005
4879828690.13181891705-708.131818917054
4976877242.27073720966444.729262790337
5071807508.13510703508-328.135107035082
5178629072.94838683614-1210.94838683614
5280438427.53605476578-384.536054765782
5383407466.60278675041873.397213249588
5466926950.59493824193-258.594938241931
551006511053.0305555986-988.030555598592
561268412884.9643811143-200.964381114252
571158711331.3381638754255.6618361246
58984310935.5776029209-1092.57760292092
5981108260.15388030792-150.153880307920
6079407795.77761992109144.222380078911
6164757108.0315756788-633.031575678803
6261216810.87029959265-689.870299592649
6396697824.334648203071844.66535179693
6477787981.86807563744-203.868075637438
6578267771.2191159778554.7808840221469
6674036510.78849694748892.211503052522
671074110310.7033617456430.296638254384
681402312749.87024233441273.12975766564
691151911617.2858987291-98.285898729071
701023610400.4553976088-164.455397608761
7180758370.82211703647-295.822117036469
7281578062.1834116001694.8165883998354







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
736917.419321421425530.465254901418304.37338794142
746654.045329618325259.384463079838048.70619615681
759213.61229434517811.2869816336110615.9376070566
767985.63973963726575.691643894349395.58783538005
777946.859855501066529.329967736299364.38974326583
787167.428241062035742.356898032538592.49958409154
7910604.65398331449172.0808847461412037.2270818826
8013488.318594194612048.282819375514928.3543690137
8111424.15819327599976.6982170498612871.6181695020
8210179.24029512298724.3940033126511634.0865869331
838090.606991588166628.411695873049552.8022873033
848040.267619402686570.760071674889509.77516713047

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 6917.41932142142 & 5530.46525490141 & 8304.37338794142 \tabularnewline
74 & 6654.04532961832 & 5259.38446307983 & 8048.70619615681 \tabularnewline
75 & 9213.6122943451 & 7811.28698163361 & 10615.9376070566 \tabularnewline
76 & 7985.6397396372 & 6575.69164389434 & 9395.58783538005 \tabularnewline
77 & 7946.85985550106 & 6529.32996773629 & 9364.38974326583 \tabularnewline
78 & 7167.42824106203 & 5742.35689803253 & 8592.49958409154 \tabularnewline
79 & 10604.6539833144 & 9172.08088474614 & 12037.2270818826 \tabularnewline
80 & 13488.3185941946 & 12048.2828193755 & 14928.3543690137 \tabularnewline
81 & 11424.1581932759 & 9976.69821704986 & 12871.6181695020 \tabularnewline
82 & 10179.2402951229 & 8724.39400331265 & 11634.0865869331 \tabularnewline
83 & 8090.60699158816 & 6628.41169587304 & 9552.8022873033 \tabularnewline
84 & 8040.26761940268 & 6570.76007167488 & 9509.77516713047 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72409&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]6917.41932142142[/C][C]5530.46525490141[/C][C]8304.37338794142[/C][/ROW]
[ROW][C]74[/C][C]6654.04532961832[/C][C]5259.38446307983[/C][C]8048.70619615681[/C][/ROW]
[ROW][C]75[/C][C]9213.6122943451[/C][C]7811.28698163361[/C][C]10615.9376070566[/C][/ROW]
[ROW][C]76[/C][C]7985.6397396372[/C][C]6575.69164389434[/C][C]9395.58783538005[/C][/ROW]
[ROW][C]77[/C][C]7946.85985550106[/C][C]6529.32996773629[/C][C]9364.38974326583[/C][/ROW]
[ROW][C]78[/C][C]7167.42824106203[/C][C]5742.35689803253[/C][C]8592.49958409154[/C][/ROW]
[ROW][C]79[/C][C]10604.6539833144[/C][C]9172.08088474614[/C][C]12037.2270818826[/C][/ROW]
[ROW][C]80[/C][C]13488.3185941946[/C][C]12048.2828193755[/C][C]14928.3543690137[/C][/ROW]
[ROW][C]81[/C][C]11424.1581932759[/C][C]9976.69821704986[/C][C]12871.6181695020[/C][/ROW]
[ROW][C]82[/C][C]10179.2402951229[/C][C]8724.39400331265[/C][C]11634.0865869331[/C][/ROW]
[ROW][C]83[/C][C]8090.60699158816[/C][C]6628.41169587304[/C][C]9552.8022873033[/C][/ROW]
[ROW][C]84[/C][C]8040.26761940268[/C][C]6570.76007167488[/C][C]9509.77516713047[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72409&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72409&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
736917.419321421425530.465254901418304.37338794142
746654.045329618325259.384463079838048.70619615681
759213.61229434517811.2869816336110615.9376070566
767985.63973963726575.691643894349395.58783538005
777946.859855501066529.329967736299364.38974326583
787167.428241062035742.356898032538592.49958409154
7910604.65398331449172.0808847461412037.2270818826
8013488.318594194612048.282819375514928.3543690137
8111424.15819327599976.6982170498612871.6181695020
8210179.24029512298724.3940033126511634.0865869331
838090.606991588166628.411695873049552.8022873033
848040.267619402686570.760071674889509.77516713047



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')